Chiang-Hsieh, Hung-Jen; Smith, Neal O; Wang, Hsin-Ju Commutative rings with toroidal zero-divisor graphs. (English) Zbl 1226.05095 Houston J. Math. 36, No. 1, 1-31 (2010). Summary: Let \(R\) be a commutative ring and let \(\Gamma (R)\) denote its zero-divisor graph. We investigate the genus number of a compact Riemann surface in which \(\Gamma(R)\) can be embedded and explicitly determine all finite commutative rings \(R\) (up to isomorphism) such that \(\Gamma (R)\) is either planar or toroidal. Cited in 31 Documents MSC: 05C10 Planar graphs; geometric and topological aspects of graph theory 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 13M05 Structure of finite commutative rings Keywords:genus number of a compact Riemann surface PDFBibTeX XMLCite \textit{H.-J. Chiang-Hsieh} et al., Houston J. Math. 36, No. 1, 1--31 (2010; Zbl 1226.05095) Full Text: arXiv Link